Miscellaneous topics that do not fit into specific categories.
Since the older messages are still visible on your laptop, this does not sound like Outlook is actually deleting them from the mailbox.
The first thing I would check on the desktop is the Cached Exchange Mode sync period.
In classic Outlook, go to:
File → Account Settings → Account Settings → select the account → Change
Then check Download email for the past / Mail to keep offline.
If it is set to 3 months, 6 months, etc., Outlook only keeps that amount of mail in the local OST file. Older messages remain on the server but may not appear normally in the local Inbox or local search.
Move the slider to All, complete the wizard, and restart Outlook.
I would also check for a local Inbox view/filter:
View → View Settings → Filter
Make sure there is no date filter or other condition hiding older messages.
A useful comparison would be to check Outlook on the web. If the older received messages are visible there, that confirms the mailbox data still exists and the issue is local to the desktop Outlook configuration.
Since AutoArchive is already disabled and the laptop still shows the messages, I would not focus on AutoArchive at this point.
If changing the sync slider to All does not resolve it, please let us know:
whether this is classic Outlook or new Outlook
the account type (Microsoft 365/Exchange, Outlook.com, IMAP, etc.)
whether the missing messages appear in Outlook on the web
what the current “Mail to keep offline” setting shows
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